Problem: Christopher is 3 times as old as Daniel. Eight years ago, Christopher was 7 times as old as Daniel. How old is Christopher now?
Explanation: We can use the given information to write down two equations that describe the ages of Christopher and Daniel. Let Christopher's current age be $c$ and Daniel's current age be $d$ The information in the first sentence can be expressed in the following equation: $c = 3d$ Eight years ago, Christopher was $c - 8$ years old, and Daniel was $d - 8$ years old. The information in the second sentence can be expressed in the following equation: $c - 8 = 7(d - 8)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $c$ , it might be easiest to solve our first equation for $d$ and substitute it into our second equation. Solving our first equation for $d$ , we get: $d = c / 3$ . Substituting this into our second equation, we get: $c - 8 = 7($ $(c / 3)$ $- 8)$ which combines the information about $c$ from both of our original equations. Simplifying the right side of this equation, we get: $c - 8 = \dfrac{7}{3} c - 56$ Solving for $c$ , we get: $\dfrac{4}{3} c = 48$ $c = \dfrac{3}{4} \cdot 48 = 36$.